© J. Christopher Beck Lecture 29: Supply Chain Scheduling 3

© J. Christopher Beck Outline Medium-term Planning Data is aggregated but still complex! Short-term Scheduling Medium-term/Short-term Integration

© J. Christopher Beck Supply Chain Scheduling

© J. Christopher Beck Supply Chain Decomposition Medium- term planning Short- term sched- uling Stage 1Stage 2Stage 3Stage 4

© J. Christopher Beck Medium-term Planning Assumptions: 4 week horizon 2 product families 3 stages: 2 factories, 1 DC, 1 customer Factories work 24/7 = 168 hours/week

© J. Christopher Beck Medium-term Planning Costs Production cost Storage cost Transportation cost Tardiness cost Non-delivery cost

Productionc p ij Cost to produce one unit of family j at factory i StoragehWeekly holding cost for one unit of any type at DC TransportationC m i2* Cost of moving one unit of any type from factory i to DC C m i*3 Cost of moving one unit of any type from factory i to the customer C m *23 Cost of moving one unit of any type from DC to the customer Tardinessw’’ j Cost per unit per week for an order of family i delivered late to DC w’’’ j Cost per unit per week for an order of family i delivered late to customer Non-delivery  Penalty cost for never delivering one unit of any product

© J. Christopher Beck Medium-term Planning Costs Production cost Storage cost Transportation cost Tardiness cost Non-delivery cost c p ij h C m i2* C m i*3 C m *23 w’’ j w’’’ j 

© J. Christopher Beck IP Objective: Minimize Production Costs x ijt = # units of family j produced at factory i in week t

© J. Christopher Beck IP Objective: Minimize Storage Costs q 2jt = # units of family j in storage at DC at end of week t

© J. Christopher Beck IP Objective: Minimize Transportation Costs y i2jt # of units of family j transported from factory i to DC in week t y i3jt # of units of family j transported from factory i to customer in week t z jt # of units of family j transported from DC to customer in week t

© J. Christopher Beck IP Objective: Minimize Tardiness Costs v 2jt = # units of family j tardy at DC at end of week t v 3jt = # units of family j tardy at customer at end of week t

© J. Christopher Beck IP Objective: Minimize Non-delivery Costs v 2j4 = # units of family j not delivered to DC at end of horizon v 3j4 = # units of family j not delivered to customer at end of horizon

© J. Christopher Beck Production Constraints Estimate processing time for 1 unit of family j at factory i Total weekly hours # units of family j produced at factory i in week t Plus storage constraints, transportation constraints, tardiness constraints, and non-delivery constraints (see P p )

© J. Christopher Beck Medium-term Planning Computes: Production amounts Storage amounts Transportation amounts

© J. Christopher Beck Short Term Scheduling Production schedule at factories what products on what machines and when? Transportation schedule between factories, DC, and customers what products on what trucks and when?

© J. Christopher Beck Short Term Scheduling For each week we know the number of items of each family that need to be produced (from x ijt ) However, that number was based on an estimate of the processing time required! In reality each product has a process plan including release date, due date, quantity, and set-ups!

© J. Christopher Beck Looks Like a “Normal” Scheduling Problem (like we’ve been studying all along) But … you are faced with the modeling problem How much of the “real world” do you represent?

© J. Christopher Beck This is Your Factory – How Do You Model It?

© J. Christopher Beck Possible Models & Components Flowshop with 5 tasks and parallel resources? Single machine? Sequence dependent setups? Buffer capacity?

© J. Christopher Beck FSP with Parallel Machines Minimize Hard problem! Setup cost if job k follows job j on machine i Weighting parameters

© J. Christopher Beck Single Machine Schedule really depends on a single bottleneck machine if the bottleneck schedule is fixed, everything else is easy May be a much easier problem in practice!

© J. Christopher Beck The Modeling Problem It is an open research question of how you take a real factory (or call centre) and create a “model” of it with optimization tools What’s the best level of detail? What can you ignore?